Question: Simplify the following expression: $\dfrac{64z^2}{88z^5}$ You can assume $z \neq 0$.
Answer: $ \dfrac{64z^2}{88z^5} = \dfrac{64}{88} \cdot \dfrac{z^2}{z^5} $ To simplify $\frac{64}{88}$ , find the greatest common factor (GCD) of $64$ and $88$ $64 = 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2 \cdot 2$ $88 = 2 \cdot 2 \cdot 2 \cdot 11$ $ \mbox{GCD}(64, 88) = 2 \cdot 2 \cdot 2 = 8 $ $ \dfrac{64}{88} \cdot \dfrac{z^2}{z^5} = \dfrac{8 \cdot 8}{8 \cdot 11} \cdot \dfrac{z^2}{z^5} $ $\phantom{ \dfrac{64}{88} \cdot \dfrac{2}{5}} = \dfrac{8}{11} \cdot \dfrac{z^2}{z^5} $ $ \dfrac{z^2}{z^5} = \dfrac{z \cdot z}{z \cdot z \cdot z \cdot z \cdot z} = \dfrac{1}{z^3} $ $ \dfrac{8}{11} \cdot \dfrac{1}{z^3} = \dfrac{8}{11z^3} $